The isomorphism between the \(\mathbb {S}^1\)  model and its purely geometric version, the m̉odel [1]}, stablishes that hidden degrees \(\kappa \)  are transformed into radial coordinates, \(r\) , which are scattered in a hyperbolic disk of radius \(R_{\mathbb {H}^2}\)  such that
\(\kappa \sim e^{(R_{\mathbb {H}^2} \ - \ r)/2} \ .\) 
